Discrete and Digital Signals and Systems - Digital Signal Processing: An Introduction with MATLAB and Applications - page 101

0

−20

−40

−60

Ω

Ω c = π / 2 π 2 π 0

1

Ω
k

0 1 2 3 4 5 6 6 7 8 9 10 16 24 32

0

Ω s /2 = π Ω s = 2 π

0

−20

−40

Ω
2 π

−60

Ω c

π 0

1

Ω
k 0 1 2 3 4 5 6 6 7 8 9 10 16 24 32

0

Ω s /2 = π Ω s = 2 π

Fig. 2.25 FIR filter design using frequency-sampling method. Above without a transition sam-
ple. Below with two transition samples (dotted curve for the first case without transition samples)

This command yields the impulse response of a length-N (i.e., order N - 1)
linear phase FIR filter with desired magnitude response, given by the vectors Fd
and Ad . Fd is a vector of normalized frequency points, ranging from 0 to 1
(corresponding to the range 0 \ f \ f s /2 Hz), and Ad contains the desired mag-
nitudes for points in Fd . Example: To design an optimal FIR filter in MATLAB
with the specifications in the previous example, one can use:

h ¼ remez ð N 1 ;½ 00 : 50 : 61 ;½ 1100 Þ

Figure ( 2.26 ) shows the actual frequency response as compared to the ad-hoc
frequency-sampling approach described in Sect. 2.6.5.2-A .